But it could also help Whole Foods attract new customers who might not have shopped there otherwise because the retailer didn't stock their favorite brands.

Whole Foods spokeswoman Brooke Buchanan acknowledged the potential changes in an email to Business Insider. She said that the company's culture will "naturally evolve" under Amazon.

"Working together with Amazon has allowed us to lower some prices and bring our natural and organic food to more people, without compromising our industry-leading quality standards," Buchanan said.

"While our culture will naturally evolve, the fundamentals of Whole Foods Market — our high-quality standards and our team members' passion, spirit of innovation, philanthropy and commitment to exceptional customer experience — will always be part of who we are and how we do business," she added. Amazon did not respond to a request for comment.

Adding items like Coca-Cola would bring Whole Foods' assortment more in line with traditional grocers like Kroger and Walmart, which in recent years have ramped up their organic offerings to become more competitive with Whole Foods.

Whole Foods has already shown a willingness to feature more conventional, non-organic products near store entrances in some of its locations, according to Barclays analysts, who have regularly visited Whole Foods stores to track changes since Amazon's takeover.

This suggests that the company is actively trying to lure more conventional customers and is experimenting with influencing shopping patterns, the analysts said in a research note.

But the strategy could backfire by alienating some of its most loyal shoppers, they said.

"On one hand, having conventional products more accessible makes a statement on pricing - since these lower-price items are more easily seen - but at the same time, this may come at the expense of the brand being seen as less relevant or authentic to some customers that value organic produce," the analysts wrote.

If Whole Foods can avoid a customer backlash, however, a shift to more conventional products — as well as popular packaged goods like Coca-Cola — could make it more competitive with Walmart, Kroger, and other traditional grocers.

"To the extent that this change were to alter price perception of the store and not alienate its core customer, this could eventually pressure competing conventional grocers," the analysts said.